A percentile is a value at or below which a given percentage or fraction of the variable values lie. It’s usually applied to large datasets. For example, an IQ of 100 is the 50th percentile for IQs because half of IQs fall below that value. You can determine the 90th percentile of a set of data points by ordering the set and counting up to the 90th percentile.

- Skill level:
- Easy

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## Instructions

- 1
Order the set of data points from lowest to highest. Count them. Denote the count by the number n.

- 2
Compute 0.9 times n, and round up to the nearest integer. Denote this number with the letter P, for percentile.

For example, for n=355, you’d compute 0.9 * 355 = 312 after rounding.

- 3
Determine the P-th data point in the set, counting from the lowest to the highest value. That point is the 90th percentile. In the previous example, the 312th point in the ordered data set is the 90th percentile, the lowest point with 90 per cent of the data points below or equal to it.

#### Tips and warnings

- Note that if the 311th point was chosen above as the 90th percentile, it wouldn’t be correct because 311/355 = 0.876, after rounding. So the data points equal to or below the 311th data point don’t constitute a full 90 per cent of the data set.
- The percentile need not be an actual data point. An alternative way to solve for the percentile when there are few numbers is to interpolate. For example, for the set {1,2,3,4}, you can define the 90th percentile to be 3.6 or 3.7, depending on what interpolation approach you choose. Interpolation is how Microsoft Excel’s percentile function works.